RetroPsychoKinesis Experiment Summary

Last updated: Monday 2019 January 21 6:00 UTC

This report is updated daily

Overall Summary

Total experiments:

401923

Number of subjects:

34670

Total tries:

411569152

Total hits:

205785978

Overall z:

0.1382

standard deviations

“Subjects” is the number of different E-mail addresses or “handles”
in the log file; there is no assurance a given individual may not
have entered a number of different identities, either intentionally
or by accident. The number of experiments includes only “for the
record” experiments, not those designated in advance by the subject
as “practice”. Since each experiment involves 1024 bits, the
total number of “Tries” in the next line is
401923×1024, or 411569152. Examination of the logged
bit sequences sent to the subjects shows that 205785978 of the
total of 411569152 bits were “Hits”—they agree with the subject's
previously-chosen goal. There were, then, 1402 more bits among a
total of 411569152 consistent with the subjects' intent to bias the
generator. This is equivalent to changing one bit in every 293558 in
the direction desired by the subject. The measured bias amounts to
0.1382 standard deviations.

Hit Histogram

The following chart summarises the results of all for-the-record
experiments (excluding runs designated in advance as "practice"
runs by the subject, which are logged for completeness, but do not
figure in the statistical analysis) performed since the RPKP
experiments were begun in January of 1997.

The blue curve gives the
normal distribution for a large number of trials of 1024 events with
probability 0.5. (For a number of trials as large as 1024, the
binomial and normal distributions are equal on the scale of this
plot.) The red boxes show the actual number of experimental runs which
resulted in the given number of hits. A “hit” is defined as the
number of bits in the 1024 bit stream which agreed with the subject's
previously chosen one-or-zero goal.

Cumulative Deviation from Expectation

Any experiment involving a random data source can be
expected to, in the absence of perturbing influences,
follow a random walk around the most probable
value. As the number of experiments increases, overall
divergences should decrease.
When examining the results of
such experiments, it's important to satisfy
yourself that any non-chance effect you observe doesn't
result from the experimenter choosing to show you
results at a peak or trough of a series which is
swinging to both sides of the chance expectation
with a mean value equal to chance. The following is a
deviation plot of the all 401923 RPKP experiments
to date; it shows the absolute divergence of the experimental
results in the direction of bias preselected by the
subject compared to that expected by chance, and the
divergence in terms of standard deviations for the cumulative number
of trials for a probability of 0.5
on each trial.

Cumulative Deviation by Intent from Expectation

Another way to evaluate the results of the experiments is to
examine how frequently the result of an experiment (excess of
one or zero bits) agrees with the subject's pre-declared goal,
regardless of the magnitude of the deviation from the mean
value. If the subject has chosen a goal corresponding to an
excess of one bits, the experiment will be scored as a success
if there is any excess of one bits at all (513 one bits out of 1024
is just as much a success as 527 one bits and, conversely, 511
one bits is as much a failure as a result of 497 one bits).
If the subject chooses a goal corresponding to an excess of zero
bits, the sense of the comparison is inverted: any excess of
zero bits is deemed a success. To preserve symmetry, results with an
equal number of zero and one bits (512 each in an experiment
of 1024 bits) are considered neutral and do not change the
cumulative result. Here we plot the cumulative deviation
by intent as z: the number of standard deviations by
which it differs from the expectation value of zero.

Runs by Subjects Histogram

The following table shows the number of experiments run by
various subjects, and the cumulative results and
standard deviation for each number of experiments.
Individual subjects who have made a large number of runs
appear show up at the bottom of the the table, and the
results they obtained can be compared.

ExperimentsRun

Number ofSubjects

Hits/Tries

z

1

13272

6786446/13590528

4.7839

2

5997

6137429/12281856

1.9968

3

3783

5808390/11621376

1.3482

4

2269

4644267/9293824

1.7352

5

1618

4143674/8284160

1.1076

6

1131

3475510/6948864

0.8179

7

816

2922774/5849088

1.4637

8

625

2560839/5120000

0.7416

9

521

2400626/4801536

0.1296

10

473

2421098/4843520

0.6016

11

361

2032371/4066304

0.7746

12

317

1947790/3895296

0.1439

13

282

1877121/3753984

0.1332

14

245

1755822/3512320

0.3607

15

214

1643174/3287040

0.3817

16

176

1443024/2883584

1.4510

17

145

1262918/2524160

1.0549

18

127

1170387/2340864

0.0588

19

123

1196104/2393088

0.5689

20

126

1291099/2580480

1.0695

21

103

1107620/2214912

0.2204

22

94

1058362/2117632

0.6240

23

76

894807/1789952

0.2526

24

68

836251/1671168

1.0319

25

71

908720/1817600

0.1187

26

62

826341/1650688

1.5520

27

67

926927/1852416

1.0565

28

47

674055/1347584

0.4531

29

52

771013/1544192

1.7430

30

52

797064/1597440

2.6205

31

40

635801/1269760

1.6347

32

47

771351/1540096

2.0999

33

44

744285/1486848

1.4122

34

39

678853/1357824

0.1013

35

30

537543/1075200

0.1099

36

40

738516/1474560

2.0357

37

37

699227/1401856

2.8733

38

40

777682/1556480

0.8945

39

26

519056/1038336

0.2198

40

37

758128/1515520

0.5979

41

30

630002/1259520

0.4313

42

21

451497/903168

0.1831

43

20

440561/880640

0.5136

44

23

518299/1036288

0.3045

45

15

344963/691200

1.5324

46

20

471054/942080

0.0288

47

18

433680/866304

1.1346

48

16

392960/786432

0.5774

49

11

276025/551936

0.1534

50

17

435050/870400

0.3216

51

23

600337/1201152

0.4361

52

20

533707/1064960

2.3780

53

13

352894/705536

0.3000

54

8

221263/442368

0.2376

55

21

592265/1182720

1.6643

56

16

459495/917504

1.5514

57

10

292299/583680

1.2016

58

11

326346/653312

0.7671

59

10

302080/604160

0.0000

60

30

921428/1843200

0.2534

61

11

343803/687104

0.6056

62

14

444388/888832

0.0594

63

16

516417/1032192

0.6319

64

10

327065/655360

1.5194

65

7

233455/465920

1.4504

66

10

337693/675840

0.5522

67

14

479734/960512

1.0652

68

7

243999/487424

0.8222

69

6

212266/423936

0.9154

70

9

322748/645120

0.4681

71

10

363437/727040

0.1947

72

8

295314/589824

1.0469

73

4

149468/299008

0.1317

74

9

340337/681984

1.5863

75

6

230329/460800

0.2092

76

7

272289/544768

0.2574

77

5

196887/394240

0.7422

78

9

359548/718848

0.2925

79

4

162173/323584

1.3396

80

5

204953/409600

0.4781

81

5

207292/414720

0.2112

82

8

335565/671744

0.7491

83

2

84897/169984

0.4608

84

2

86078/172032

0.2990

85

2

87098/174080

0.2780

86

5

220155/440320

0.0151

87

2

88863/178176

1.0661

88

7

315248/630784

0.3626

89

2

91526/182272

1.8270

90

2

91843/184320

1.4767

91

3

139739/279552

0.1400

92

6

282565/565248

0.1570

93

3

143124/285696

1.0327

94

4

193053/385024

1.7437

95

6

291301/583680

1.4110

96

2

98517/196608

0.9607

97

3

149407/297984

1.5205

98

2

100457/200704

0.4688

99

4

202582/405504

0.5339

100

7

358282/716800

0.2787

101

6

310369/620544

0.2463

102

3

157014/313344

1.2219

103

2

105203/210944

1.1714

104

4

212949/425984

0.1318

105

1

53849/107520

0.5428

106

2

108628/217088

0.3606

107

2

109199/219136

1.5765

108

6

332114/663552

0.8299

109

2

111567/223232

0.2074

110

2

112340/225280

1.2641

111

3

170848/340992

1.2056

112

4

229540/458752

0.4843

113

2

115537/231424

0.7276

114

8

467438/933888

1.0224

115

3

176845/353280

0.6898

116

8

475162/950272

0.0533

117

2

120024/239616

0.8825

118

4

241043/483328

1.7865

119

2

122043/243712

0.7576

120

5

307260/614400

0.1531

121

2

124061/247808

0.6308

122

4

249676/499712

0.5093

123

2

125473/251904

1.9087

124

1

63580/126976

0.5164

125

1

63928/128000

0.4025

126

2

128874/258048

0.5906

127

3

195268/390144

0.6276

128

1

65799/131072

1.4529

129

3

198940/396288

2.5289

130

6

399670/798720

0.6937

132

2

135184/270336

0.0615

133

2

136383/272384

0.7319

134

2

137337/274432

0.4620

135

3

207396/414720

0.1118

136

3

208849/417792

0.1454

137

1

69880/140288

1.4097

138

2

141170/282624

0.5342

139

2

142191/284672

0.5435

140

4

286640/573440

0.2113

141

2

144591/288768

0.7704

142

1

72469/145408

1.2325

143

2

146331/292864

0.3733

144

2

147321/294912

0.4972

145

3

222983/445440

0.7881

146

3

224706/448512

1.3439

148

2

151121/303104

1.5657

149

4

304741/610304

1.0522

150

3

230294/460800

0.3123

151

2

154761/309248

0.4927

153

3

235312/470016

0.8868

154

1

79013/157696

0.8310

155

2

158985/317440

0.9407

157

1

80384/160768

0.0000

158

1

80734/161792

0.8055

159

5

406721/814080

0.7071

160

2

164434/327680

2.0754

161

3

247386/494592

0.2559

162

3

249378/497664

1.5479

164

1

83847/167936

0.5905

165

2

168697/337920

0.9049

166

2

170189/339968

0.7032

170

1

86917/174080

0.5896

171

2

174975/350208

0.4360

172

3

264141/528384

0.1403

174

2

178518/356352

1.1458

175

5

447708/896000

0.6170

176

2

180539/360448

1.0493

177

1

90903/181248

1.3107

178

1

90860/182272

1.2929

179

1

91794/183296

0.6820

180

1

92118/184320

0.1957

181

1

92328/185344

1.5981

182

1

93122/186368

0.2872

183

1

93828/187392

0.6099

184

1

94435/188416

1.0459

186

2

190331/380928

0.4310

187

1

95583/191488

0.7358

188

1

96634/192512

1.7230

189

3

290190/580608

0.2992

190

2

194666/389120

0.3399

191

1

97737/195584

0.2487

192

2

196641/393216

0.1053

194

1

99376/198656

0.2154

195

1

99196/199680

2.8824

196

1

100383/200704

0.1384

197

2

201524/403456

0.6423

200

2

204715/409600

0.2656

201

2

205561/411648

0.8198

202

1

103444/206848

0.0879

204

2

209659/417792

2.3609

205

1

105150/209920

0.8294

208

2

213287/425984

0.9040

210

1

107717/215040

0.8496

212

2

217415/434176

0.9925

217

3

332997/666624

0.7716

219

1

112187/224256

0.2492

224

1

114861/229376

0.7224

225

1

115213/230400

0.0542

227

3

349082/697344

0.9820

229

1

117253/234496

0.0207

232

1

118732/237568

0.2134

234

1

120044/239616

0.9642

235

2

240535/481280

0.3027

236

1

120846/241664

0.0570

238

1

121802/243712

0.2188

240

2

245319/491520

1.2581

241

1

123381/246784

0.0443

245

1

125995/250880

2.2161

250

1

128051/256000

0.2016

251

1

128793/257024

1.1085

252

2

258266/516096

0.6069

253

1

129800/259072

1.0373

258

1

132534/264192

1.7043

259

2

265473/530432

0.7057

262

1

134337/268288

0.7452

272

1

139725/278528

1.7470

276

1

141824/282624

1.9262

277

1

141398/283648

1.5997

278

1

142232/284672

0.3898

280

1

143009/286720

1.3110

282

1

144776/288768

1.4590

283

1

144948/289792

0.1932

284

1

145732/290816

1.2016

286

1

146644/292864

0.7835

291

1

149196/297984

0.7474

292

1

150030/299008

1.9239

295

1

151495/302080

1.6557

296

1

151540/303104

0.0436

302

1

154387/309248

0.8524

306

2

312030/626688

3.3197

307

1

156831/314368

1.2592

312

1

160124/319488

1.3446

313

1

160538/320512

0.9962

315

1

160439/322560

2.9616

321

1

164988/328704

2.2186

330

1

169191/337920

0.7948

332

1

169748/339968

0.8095

342

1

175610/350208

1.7101

343

1

175927/351232

1.0495

346

1

177270/354304

0.3965

348

1

178012/356352

0.5495

349

1

178566/357376

0.4082

357

1

182946/365568

0.5359

367

1

188165/375808

0.8515

368

1

188552/376832

0.4431

375

1

192355/384000

1.1458

381

1

195222/390144

0.4803

382

1

195449/391168

0.4317

383

1

196677/392192

1.8555

401

2

411195/821248

1.2602

404

1

206995/413696

0.4571

416

1

213097/425984

0.3218

423

1

216977/433152

1.2186

435

1

222783/445440

0.1888

437

1

224495/447488

2.2453

438

1

223835/448512

1.2573

440

1

225551/450560

0.8075

444

1

226855/454656

1.4030

445

1

228040/455680

0.5926

449

1

230059/459776

0.5044

454

1

231895/464896

1.6221

455

1

232814/465920

0.4278

456

1

233269/466944

0.5941

457

1

233366/467968

1.8068

465

1

238314/476160

0.6782

477

1

244153/488448

0.2032

479

1

245108/490496

0.3998

483

1

248038/494592

2.1101

486

1

248975/497664

0.4054

498

1

255021/509952

0.1260

500

2

512273/1024000

0.5396

504

1

258187/516096

0.3870

521

1

267573/533504

2.2480

525

1

269535/537600

2.0049

527

1

270066/539648

0.6589

531

1

271399/543744

1.2829

539

1

275737/551936

0.6219

555

1

283962/568320

0.5253

579

1

296000/592896

1.1636

598

1

306822/612352

1.6511

617

1

315662/631808

0.6089

618

1

316245/632832

0.4299

622

1

319329/636928

2.1677

631

1

323423/646144

0.8733

659

1

337721/674816

0.7620

670

1

343489/686080

1.0841

672

1

344395/688128

0.7980

698

1

357541/714752

0.3903

708

1

362383/724992

0.2654

724

1

371383/741376

1.6143

748

1

383207/765952

0.5279

765

1

390911/783360

1.7377

787

1

402579/805888

0.8132

792

1

405199/811008

0.6774

802

1

410228/821248

0.8740

833

1

427130/852992

1.3729

847

1

434412/867328

1.6063

864

1

442760/884736

0.8335

902

1

461910/923648

0.1790

973

1

498360/996352

0.3687

992

2

1015929/2031616

0.1698

1005

1

514573/1029120

0.0256

1024

1

523462/1048576

1.6133

1027

1

525719/1051648

0.2048

1101

1

563674/1127424

0.0716

1234

1

631349/1263616

0.8166

1241

1

635247/1270784

0.2573

1261

1

645933/1291264

0.5298

1349

1

690715/1381376

0.0459

1360

1

695800/1392640

0.8813

1407

1

719699/1440768

1.1414

1458

1

746586/1492992

0.1473

1481

1

758020/1516544

0.4093

1645

1

841693/1684480

0.8429

1652

1

846016/1691648

0.2952

1742

1

891790/1783808

0.1707

1769

1

906121/1811456

0.5840

1947

1

996742/1993728

0.1728

2000

1

1024947/2048000

1.3235

2198

1

1126814/2250752

1.9170

2257

1

1156265/2311168

0.8959

2296

1

1174949/2351104

0.7865

2325

1

1190043/2380800

0.4627

2591

1

1327380/2653184

0.9675

4210

1

2154581/4311040

0.9045

4223

1

2161820/4324352

0.3424

4261

1

2181516/4363264

0.1111

4601

1

2355712/4711424

0.0000

4731

1

2422549/4844544

0.2517

5250

1

2689581/5376000

1.3637

5724

1

2929525/5861376

0.9607

6371

1

3259087/6523904

2.2434

6565

1

3361825/6722560

0.4204

8116

1

4155091/8310784

0.2088

8325

1

4262913/8524800

0.3514

12038

1

6162776/12326912

0.3874

12950

1

6631971/13260800

0.8628

16834

1

8618203/17238016

0.3878

Results by Visual Feedback Program

Feedback Program

Runs

Hits/Tries

z

bellcurve

196538

100629263/201254912

0.2548

clockface

96253

49278450/98563072

0.6217

experiment

998

510302/1021952

1.3334

pendulum

108134

55367963/110729216

0.6377

The table at the right shows results obtained by all subjects, sorted
by the visual feedback program they selected.

Results by Goal

Goal

Runs

Hits/Tries

z

0

90077

46121887/92238848

0.5129

1

311840

159661074/319324160

0.1126

Each visual feedback program allows the user to choose a goal
which corresponds to either an excess of zero or one bits in
the data stream. The following table gives results by goal,
indicating how many times each goal was chosen. The default
goal is an excess of one bits.